Question

vector w has magnitude 25.0 and direction angle 41.7 degrees. Calculate the horizontal and vertical components of w

Answer 1

Consider the attached picture. It represents a vector, centered in the origin with angle 41.7 degrees, and a circumference with radius 25, centered in the origin.

As you can see, the horizontal and vertical components of the vector correspond to the lengths of segments OD and OC, respectively.

You might recognize this scenario from you trigonometry class: if the circle had radius 1, we would have

$OD=\cos(41.7),\quad OC=\sin(41.7)$

Since the circle has radius 25, we have to scale those coordinates:

$OD=25\cos(41.7),\quad OC=25\sin(41.7)$